Russia and other large oil producers will next month discuss relaxing an agreement that has cut output and helped support crude prices—a move that could relieve some of that price pressure in coming weeks.

Russian Oil Minister Alexander Novak said he would discuss with counterparts from Saudi Arabia and other members of the Organization of the Petroleum Exporting Countries the possibility of a “gradual output recovery,” according to RIA, a Russian state news agency. The talks will take place during a scheduled OPEC meeting...